OFFSET
1,1
COMMENTS
This polynomial f(n) generates 28 consecutive prime numbers for n = 0 to n = 27.
In n^2 + n + 41, substitute n -> 3*n^3 - 134*n^2 + 1980*n - 9663.
REFERENCES
P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 137.
LINKS
Carlos Rivera, Puzzle 232, The Prime Puzzles & Problems Connection.
Eric Weisstein's World of Mathematics, Prime-generating polynomial.
EXAMPLE
f(1) = 9(1)^6 - 804(1)^5 + 29836(1)^4 - 588615(1)^3 + 6509950(1)^2 - 38263500(1) + 93363947 = 61050823, a prime number.
MATHEMATICA
f[n_] := 9n^6-804n^5+29836n^4-588615n^3+6509950n^2-38263500n+93363947; f[Select[Range[0, 100], PrimeQ[f[ # ]] &]] (* Stefan Steinerberger, Apr 16 2006 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Parviz Afereidoon (afereidoon(AT)gmail.com), Apr 08 2006
EXTENSIONS
Edited by Don Reble, Apr 14 2006
More terms from Petros Hadjicostas, Nov 04 2019
STATUS
approved